I think it says “or” to reinforce “two (but not more than two) dwellings” in the preamble. It ensures that you cannot simultaneously rely on different subparagraphs to cover more than two dwellings in different combinations.
Imagine a Venn diagram where one ring contains the original home you have left through fear of violence plus the refuge you are currently staying in, while the other ring contains the refuge and the new tenancy awaiting adaptations. There might be a period in which you satisfy subparas (a), (d) and (e) all at the same time, while having three liabilities. You would only be able to rely on one of the subparas to cover two dwellings at any one time.
I don’t think “or” prevents different subparas from applying consecutively – at all times, you are only applying one of them. Suppose the claimant relied on (e) at the start of the tenancy, then had a routine overlap a year later at the end of the tenancy – you wouldn’t say (d) cannot apply because (e) once did. You’d say thus is a different period and a different situation. Your case is no different in principle, it’s just that the two periods are closer together.
